Math
Composition of functions.
Definition
Composition of functions is the process of applying one function to the result of another. Written as (f ∘ g)(x) = f(g(x)), you first evaluate the inner function g(x), then use that output as the input for f.
How it works · 3 phases
Step by step.
- Identify the inner function g(x) and outer function f(x)
- Substitute g(x) into every x in f(x)
- Simplify the resulting expression
Examples
Real-world.
- 1 If f(x) = 2x + 1 and g(x) = x², then f(g(3)) = f(9) = 19
- 2 A store applies a 20% discount then 8% tax — that's a composition of two functions
- 3 Converting Celsius to Fahrenheit, then Fahrenheit to Rankine